OSI alone does not yield relative-error guarantees for sketching; counterexamples for least-squares and randomized SVD show that upper control on the optimal residual is required to recover near-relative error.
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Oblivious Subspace Injection Is Not Enough for Relative Error
OSI alone does not yield relative-error guarantees for sketching; counterexamples for least-squares and randomized SVD show that upper control on the optimal residual is required to recover near-relative error.